Both Houseknecht (1987) and Wilson and McBride (1988) are to be commended for painstaking and highly quantitative studies of an aspect of sandstone diagenesis that is all too often overlooked. However, two problems with their work exist: (1) an incorrect formula has been used for analysis of compactional porosity loss, and (2) the assumption of a value of 40% for the original porosity of sandstone is an unnecessary oversimplification. Nevertheless, neither of these problems significantly alters the fundamental conclusions reported in these excellent papers.

CALCULATION OF POROSITY LOST BY COMPACTION

Both Houseknecht (1987) and Wilson and McBride (1988) commit the same fundamental error in evaluating the amount of original porosity lost by compactional processes in sandstone (see Table 1 for definitions of terminology used in this discussion). The error is that the compactional porosity loss (COPL) is calculated as the difference between the original porosity (OP) and the present intergranular volume (IGV), as determined by point counting petrographic thin sections:

EQUATION (1)

The reason that this seemingly straightforward formula is wrong is that the total volume of the sandstone changes during compaction, such that present percent intergranular volume (IGV) is a percentage of a different and smaller total rock volume than the original porosity (OP). Subtraction of one from the other, therefore, is meaningless, or, at best, provides a systematically inaccurate approximation.

This problem is illustrated in Figure 1. The bar diagram at the left represents 100 volume units (say, 100 cm³) of a sandstone with 40% intergranular volume. This rock volume consists of 60 cm³ of solid mineral matter and 40 cm³ of pore space. Compaction of this rock could yield the rock represented by the bar diagram on the right, consisting of the same 60 cm³ of solid mineral matter and only 20 cm³ of intergranular pore space. The porosity (equal to percent intergranular volume) of the compacted rock is now 25%. The compactional porosity loss is 20%, so that exactly 50% of the original 40% porosity has been

Fig. 1. Bar diagrams representing change in total rock volume and porosity attending compaction of given volume of sandstone. Each sample consists of solid grains (represented by vertical ruled volumes) and intergranular porosity (unpatterned volumes). Before compaction (left), rock comprises 60 cm³ grains and 40 cm³ of pore space. After compaction (right) rock has same grain volume, but less total volume, pore volume, and percent porosity (^phgr).

lost by compaction (the relative percent compactional porosity loss). However, for this same example, equation 1 would calculate the compactional porosity loss to be 40% - 25% = 15%, which is 37.5% of the original 40% porosity.

The correct formula for calculation of the compactional porosity loss of a sandstone is:

EQUATION (2)

The amount of original porosity destroyed by cementation, the cementational porosity loss (CEPL), is also a function of the degree of compaction and can be calculated from the ratio of the present volume percent cement (CEM) to the intergranular volume:

EQUATION (3)

Certain corrections to Houseknecht's (1987) very useful volume-cement diagram are therefore necessary, as shown in Figure 2.

ORIGINAL POROSITY OF SANDSTONE

The second objection concerns the value of 40% used for the original porosity of sandstone by both Houseknecht (1987) and Wilson and McBride (1988). Beard and Weyl (1973) demonstrated that porosity of wet

Fig. 2. Suggested modification of volume-cement diagram proposed by Houseknecht (1987) for evaluation of relative importance of compactional processes and cementation to porosity development of sandstone. Diagonal dashed line in each plot represents set of points where equal amounts of original porosity have been lost to compaction and cementation. Vertical scale along right side of each plot is equivalent to relative percent compactional porosity loss, defined in Table 1. Scales along bottom and right axes are valid only if original porosity is assumed to be 40%. (A) Original diagram from Figure 4 of Houseknecht (1987). Scales given on bottom and right axes are incorrect. (B) Corrected version. Amount of original porosity destroyed by cementation is not fixed function of percent ceme t only, but varies with percent intergranular volume as indicated by dotted lines.

Fig. 3. Variation of porosity of wet packed sand with Trask sorting coefficient, based on data from Beard and Weyl (1973). Using artificial mixtures of natural sands of known sorting, Beard and Weyl showed that porosity varies with sorting, but not with grain size.

packed sand decreases markedly as sorting becomes poorer, but is little dependent on variations in grain size. The approximate relationship is shown in Figure 3. This data set is applicable only for arenites with low detrital matrix content, but this restriction includes most sandstones that serve as economic hydrocarbon reservoirs.

Values of Trask sorting coefficient and, thus, of original porosity can be very easily estimated from thin section using the comparator photomicrographs of Beard and Weyl (1973). Assumption of an original porosity value of 40% for all sandstone samples thus appears to introduce an unnecessary distortion into the quantitative analysis of sandstone compaction.

Houseknecht (1987, p. 640) concluded "that sorting appears to have played an insignificant role in determining intergranular volume" because he found no differences in present intergranular volume between well-sorted and moderately sorted sandstones that had undergone extensive amounts of compaction. However, the fact that variations in sorting may be of secondary importance to other parameters in determining the response of sandstones to compaction does not mean that variations in sorting are not of primary importance in determining the original porosity of sandstones.

If the assumption of 40% original porosity for all sandstones is abandoned, then the present percentages of intergranular volume and cement no longer have a constant relationship to original porosity, and Houseknecht's (1987) volume-cement diagram (Figure 2) can no longer be interpreted in terms of the relative percentages of original porosity destroyed by compaction and cementation. However, it is a simple task to use Figure 3 together with equations 2 and 3 to replot thin section analyses of Trask sorting coefficient, percent intergranular volume, and percent intergranular cement as a rigorous diagram of compactional porosity loss vs. cementational porosity loss.

Table 1. Definitions of Terminology Applied to Sandstones in this Discussion

AAPG Search and Discovery Article #91023©1989 AAPG Eastern Section, Sept. 10-13, 1989, Bloomington, Indiana.